Solow model lecture 1
“SOME FACTS
ABOUT PROSPERITY
AND GROWTH”
INTRODUCTION
•
How do we measure prosperity? In economics, often by GDP per
person!
•
Higher income means higher consumption or higher saving (possibly
both) and saving can be used for future consumption. Consumption
is always rooted in income and is a decent proxy for well being.
•
In this course we often consider growth of income per person
because the way to reach a high level of income per person is
through a process of high growth in income per person.
•
Relatively small differences in growth rates can imply large
differences in levels over long periods as evidenced by next slide.
•
Conclusion: Growth is important! One focus of our classes is What
creates growth?
COMPARING THE GDP LEVELS OF TWO COUNTRIES
•
Purchasing power adjustment:
–
When converting, say, pesos into US dollars, we want to take into
account differences in the costs of living in the two countries.
–
Hence, the relevant rate of conversion should reflect that
consumer goods are usually much cheaper in less developed
countries.
•
Per worker or per capita?
–
GDP per capita = Official GDP divided by total population:
Underestimates the production of less developed countries, since
they typically have a larger share of the population working outside
the official market economy.
–
GDP per worker = Official GDP divided by the labour force
(population times participation rate): corrects for differences in
participation rates, hence it is more of a productivity measure.
BALANCED GROWTH
•
summarizes stylized facts 5 7 and is an important
concept for evaluating the growth models in the
subsequent chapters.
•
A growth process follows balanced growth if:
1.
GDP per worker, consumption per worker, the real
wage and the capital intensity all grow at one and the
same constant rate, g.
2.
The labour force (population) grows at a constant
rate, n.
3.
GDP, consumption and capital grow at the common
rate, g+n.
4.
The capital ouput ratio and the rate of return on
capital are constant.
“CAPITAL
ACCUMULATION AND
GROWTH: THE
BASIC SOLOW
MODEL”
THE BASIC SOLOW MODEL
•
How can a nation become rich, i.e., initiate a growth
process leading to higher GDP/consumption per capita
in the long run?
•
The basic Solow model provides some first answers:
It predicts how the evolution and the long run levels
of GDP and consumption per capita depend on
structural parameters such as the rate of investment
and the growth rate of the labour force.
•
Key elements of the Solow model:
–
In each period, output is determined by the supplies of
capital and labour through the production function.
–
Exogenous savings/investment rate, s , exogenous growth
rate of labour force, n , and exogenous depreciation rate, δ
–
Explicit description of capital accumulation:
–
Accumulation of capital is the main driving force for wealth.
“Basic” model: No technological progress
THE ”MICRO WORLD” OF THE SOLOW MODEL
• Object: Closed economy
• Time: A sequence of periods/years
• Agents: Households and firms (and government)
• Commodities and markets: Output, capital
services and labour services (one asset = physical
capital)
• The market for output: Supply = firms’ output, .
Demand from households for consumption and
investment = . Relative price = 1.
– One-sector model: Output can be used either for
consumption or for investment.
• The market for capital services: Consumers own
the capital stock, , and rent its services to firms.
Supply of capital services = . Firms’ demand =
– Relative price (in units of output) for renting one unit of
capital for one period: = real rental rate for capital
– Real interest rate: , where is the rate of
depreciation, or:
(Alternative interpretation: The firms own the capital,
borrow for the purchase of capital at an interest rate of
and bear the cost of depreciation themselves.)
– User cost
• Labour market: Households supply = = the
labour force. Demand from firms = . Relative
price: = the real wage rate.
• Competitive markets: and adjust to equate
supply and demand in all markets full (or natural)
utilization of resources.
“CAPITAL
ACCUMULATION AND
GROWTH: THE BASIC
SOLOW MODEL”
The essential assumption underlying the Solow model
interpreted to include a government is that the sum
of private and public consumption as a fraction
of GDP is a constant 1 minus s
STRUCTURAL POLICY
1. Crowding out:
• Consider a permanent fall in caused by a permanent
increase in government consumption as a percentage of
GDP.
• What happens on impact? is unaffected and still grows
at the rate of , and is unaffected. But savings decrease
and consumption increases. There is full crowding out.
• What happens in the longer run? During a transitional
period grows more slowly than at the rate of and
falls down to a new lower steady state level. There is more
than full crowding out. And the real interest rate
increases.
• The government cannot increase GDP by raising
government expenditure in the long run. How about the
short run? (Keynes…
Motives for tax financed public services from a long
run perspective
•
Public investments (that would not be made by private
agents)
For government consumption:
•
Public (non rival and possibly non excludable) goods
•
Public consumption, e.g., on education and health care,
replacing private consumption, which means that is not
affected
•
Distributive reasons
•
Externalities (education)
•
General productivity effects of public consumption, e.g.,
judicial system, health care, etc.
GROWTH IN THE BASIC SOLOW MODEL
• The long run prediction of the Solow model is its
steady state. What is the growth rate of GDP per
capita in steady state?
• Zero! Not in accordance with stylized facts.
GDP grows, but only at the same
rate as the labour force. Why is that?
However, there is transitory growth. How long-lasting
is that?
In the Solow model, the transition towards steady
state is at least as important as the steady state
itself. And during this transition there is growth in
and . Hence, the basic Solow model is a
growth model!
Growth in GDP per worker is higher the further below
steady state the economy is. This is in accordance
with conditional convergence
•
A permanent increase in gives a jump upwards in
the growth rate of GDP per worker.
CONCLUSIONS BASED ON THE BASIC SOLOW
MODEL
•
What can a (poor) country do to create a transitory
growth in GDP per worker resulting in a permanently
higher level of income and consumption per worker?
The basic Solow model provides the following
answers:
–
Increase the savings rate
–
Reduce the growth rate of the labour force
–
Reduce the rate of depreciation, i.e., invest better
–
Improve the level of technology
•
How useful are these recommendations?
ABOUT PROSPERITY
AND GROWTH”
INTRODUCTION
•
How do we measure prosperity? In economics, often by GDP per
person!
•
Higher income means higher consumption or higher saving (possibly
both) and saving can be used for future consumption. Consumption
is always rooted in income and is a decent proxy for well being.
•
In this course we often consider growth of income per person
because the way to reach a high level of income per person is
through a process of high growth in income per person.
•
Relatively small differences in growth rates can imply large
differences in levels over long periods as evidenced by next slide.
•
Conclusion: Growth is important! One focus of our classes is What
creates growth?
COMPARING THE GDP LEVELS OF TWO COUNTRIES
•
Purchasing power adjustment:
–
When converting, say, pesos into US dollars, we want to take into
account differences in the costs of living in the two countries.
–
Hence, the relevant rate of conversion should reflect that
consumer goods are usually much cheaper in less developed
countries.
•
Per worker or per capita?
–
GDP per capita = Official GDP divided by total population:
Underestimates the production of less developed countries, since
they typically have a larger share of the population working outside
the official market economy.
–
GDP per worker = Official GDP divided by the labour force
(population times participation rate): corrects for differences in
participation rates, hence it is more of a productivity measure.
BALANCED GROWTH
•
summarizes stylized facts 5 7 and is an important
concept for evaluating the growth models in the
subsequent chapters.
•
A growth process follows balanced growth if:
1.
GDP per worker, consumption per worker, the real
wage and the capital intensity all grow at one and the
same constant rate, g.
2.
The labour force (population) grows at a constant
rate, n.
3.
GDP, consumption and capital grow at the common
rate, g+n.
4.
The capital ouput ratio and the rate of return on
capital are constant.
“CAPITAL
ACCUMULATION AND
GROWTH: THE
BASIC SOLOW
MODEL”
THE BASIC SOLOW MODEL
•
How can a nation become rich, i.e., initiate a growth
process leading to higher GDP/consumption per capita
in the long run?
•
The basic Solow model provides some first answers:
It predicts how the evolution and the long run levels
of GDP and consumption per capita depend on
structural parameters such as the rate of investment
and the growth rate of the labour force.
•
Key elements of the Solow model:
–
In each period, output is determined by the supplies of
capital and labour through the production function.
–
Exogenous savings/investment rate, s , exogenous growth
rate of labour force, n , and exogenous depreciation rate, δ
–
Explicit description of capital accumulation:
–
Accumulation of capital is the main driving force for wealth.
“Basic” model: No technological progress
THE ”MICRO WORLD” OF THE SOLOW MODEL
• Object: Closed economy
• Time: A sequence of periods/years
• Agents: Households and firms (and government)
• Commodities and markets: Output, capital
services and labour services (one asset = physical
capital)
• The market for output: Supply = firms’ output, .
Demand from households for consumption and
investment = . Relative price = 1.
– One-sector model: Output can be used either for
consumption or for investment.
• The market for capital services: Consumers own
the capital stock, , and rent its services to firms.
Supply of capital services = . Firms’ demand =
– Relative price (in units of output) for renting one unit of
capital for one period: = real rental rate for capital
– Real interest rate: , where is the rate of
depreciation, or:
(Alternative interpretation: The firms own the capital,
borrow for the purchase of capital at an interest rate of
and bear the cost of depreciation themselves.)
– User cost
• Labour market: Households supply = = the
labour force. Demand from firms = . Relative
price: = the real wage rate.
• Competitive markets: and adjust to equate
supply and demand in all markets full (or natural)
utilization of resources.
“CAPITAL
ACCUMULATION AND
GROWTH: THE BASIC
SOLOW MODEL”
The essential assumption underlying the Solow model
interpreted to include a government is that the sum
of private and public consumption as a fraction
of GDP is a constant 1 minus s
STRUCTURAL POLICY
1. Crowding out:
• Consider a permanent fall in caused by a permanent
increase in government consumption as a percentage of
GDP.
• What happens on impact? is unaffected and still grows
at the rate of , and is unaffected. But savings decrease
and consumption increases. There is full crowding out.
• What happens in the longer run? During a transitional
period grows more slowly than at the rate of and
falls down to a new lower steady state level. There is more
than full crowding out. And the real interest rate
increases.
• The government cannot increase GDP by raising
government expenditure in the long run. How about the
short run? (Keynes…
Motives for tax financed public services from a long
run perspective
•
Public investments (that would not be made by private
agents)
For government consumption:
•
Public (non rival and possibly non excludable) goods
•
Public consumption, e.g., on education and health care,
replacing private consumption, which means that is not
affected
•
Distributive reasons
•
Externalities (education)
•
General productivity effects of public consumption, e.g.,
judicial system, health care, etc.
GROWTH IN THE BASIC SOLOW MODEL
• The long run prediction of the Solow model is its
steady state. What is the growth rate of GDP per
capita in steady state?
• Zero! Not in accordance with stylized facts.
GDP grows, but only at the same
rate as the labour force. Why is that?
However, there is transitory growth. How long-lasting
is that?
In the Solow model, the transition towards steady
state is at least as important as the steady state
itself. And during this transition there is growth in
and . Hence, the basic Solow model is a
growth model!
Growth in GDP per worker is higher the further below
steady state the economy is. This is in accordance
with conditional convergence
•
A permanent increase in gives a jump upwards in
the growth rate of GDP per worker.
CONCLUSIONS BASED ON THE BASIC SOLOW
MODEL
•
What can a (poor) country do to create a transitory
growth in GDP per worker resulting in a permanently
higher level of income and consumption per worker?
The basic Solow model provides the following
answers:
–
Increase the savings rate
–
Reduce the growth rate of the labour force
–
Reduce the rate of depreciation, i.e., invest better
–
Improve the level of technology
•
How useful are these recommendations?
Comments
Post a Comment